Interference phenomena due to a double bend in a ~~aflt~~ wire

Experimental studies of the conductance properties of split-gate field-effect transistors have evidenced quantum wave guide effects for electron propagation through such structures.‘-3 Since then, a number of studies in such structures have been reported which have shown effects associated with resonant tunneling through impurities,4 superlattice effects due to a periodic grating,5 and single electron charging phenomena6 just to mention a few. Quantum interference phenomena are only apparent when the path length of electrons is below the inelastic mean free path. However, clear quantum waveguide effects due to artificial electron confinement may only be distinguished when the mean free path associated with elastic scattering (e.g., due to impurities and defects) is more than the dimensions of the waveguide itself. Thus, nanometer scale geometries and high mobility samples are necessary for the resolution of electron diffraction effects. In this letter, the low-temperature conductance properties of a narrow constriction in a high-mobility two-dimensional electron gas with a doublebend discontinuity are reported, and evidence for interference effects due to the bend are shown. The theoretical effects of bend discontinuities on the transmission coefficient and current voltage characteristics of quantum wire structures have been reported by several groups. ‘-lo The effect of a double-bend discontinuity has been discussed in detail using a mode-matching theory by Weisshaar et ~1.~‘~’ There it was shown that strong resonance effects are present in the transmission coefficient versus energy due to the presence of a perpendicular single right angle bend. The effect of a double bend is to add further fine resonance features superimposed on the dominant resonance, with width and spacing in energy being dependent on the length of the bend. To study the effect of bends on the conductance properties of quantum waveguide structures, the double-bend structure shown in Fig. 1 was fabricated, Here, a split-gate structure was utilized as shown in Fig. 1 (a) in which the depletion region between the gate electrodes is used to constrict the electronic motion in the channel. The basic structure consists of a single Alo,27G%.73As/GaAs interface grown on undoped GaAs where the AlGaAs layer was doped 1 x 10’8/cm3 with a 150 i spacer layer. The twodimensional electron gas density in the unprocessed material was measured to be 3.8~ lO*‘/cm* with a mobility in excess of 9 X lo5 cm*/V s at 1.7 K based on Hall and Shubnikov-de Haas measurements. Depletion mode modulation-doped field-effect transistors ( MODFETs) with and without split gates were fabricated via conventional optical lithography using Au/Ge ohmics to define the source and drain regions, and Ti/Au for the bonding pads. The transistors were mesa etched for isolation. After the ohmic contact deposition and anneal, electron beam lithography was used to define the double-bend split-gate structures used in this work.” Following thermal deposition of 5 nm titanium and 25 nm gold, the gate pattern was transferred to the heterostructure by a lift-off procedure. The final gates have an overall length of 0.5 pm and a channel width of 0.1 pm, as shown in Fig. 1 (bl . Conductance measurements were made over the temperature range O.OT--5 K using a low-frequency (28.6 Hz) bridge arrangement in which the voltage across the sample